Simplify (x^16y^0z^8)^(1/4)

${(x^{16} y^{0} z^{8})}^{\frac{1}{4}}$

Step 1

Anything raised to $0$ is $1$ .

${(x^{16} \cdot 1 z^{8})}^{\frac{1}{4}}$

Step 2

Multiply $x^{16}$ by $1$ .

${(x^{16} z^{8})}^{\frac{1}{4}}$

Step 3

Apply the product rule to $x^{16} z^{8}$ .

${(x^{16})}^{\frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 4

Multiply the exponents in ${(x^{16})}^{\frac{1}{4}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{16 (\frac{1}{4})} {(z^{8})}^{\frac{1}{4}}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$x^{4 (4) \frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Cancel the common factor.

$x^{4 \cdot 4 \frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Rewrite the expression.

$x^{4} {(z^{8})}^{\frac{1}{4}}$

Step 5

Multiply the exponents in ${(z^{8})}^{\frac{1}{4}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{4} z^{8 (\frac{1}{4})}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$x^{4} z^{4 (2) \frac{1}{4}}$

Cancel the common factor.

$x^{4} z^{4 \cdot 2 \frac{1}{4}}$

Rewrite the expression.

$x^{4} z^{2}$